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Sonobe 12片折纸八面体

Sonobe 12片折纸八面体
几何画板及绘图内容加载中，请稍等……
2017-05-03 04:10
多边形变换几何作图
该范例展示了Sonobe 12片折纸八面体的几何构造。涉及的核心数学概念包括多边形、变换和几何作图。通过使用GeoGebra命令如Intersect、Point、Circle、LineBisector等，可以动态地展示八面体的构造过程。适合用于初中或高中几何教学，帮助学生理解多面体的构造和变换。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(B, A) → p
  4. LineBisector(A, B) → e
  5. Polygon(A, B, 3) → poly1, a, b, d, C
  6. LineBisector(A, C) → f
  7. Intersect(f, d) → K
  8. Intersect(e, f) → D
  9. Dilate(K, fac, D) → K'
  10. OrthogonalLine(D, xOyPlane) → g
  11. Point(g) → E
  12. Circle(A, B) → c
  13. Intersect(c, p, 1) → J
  14. Polygon(B, J, E) → poly3, e_2, b_2, j_1
  15. Intersect(b_2, e) → L
  16. Octahedron(A, B, C) → h, F, faceCGH, faceFGH, edgeAC, edgeAB, edgeBC, edgeAH, edgeCH, edgeAF, edgeFH, edgeBF, G, edgeBG, edgeFG, edgeCG, edgeGH, H, faceABC, faceACH, faceAFH, faceABF, faceBFG, faceBCG
  17. Plane(F, H, C) → i
  18. Mirror(E, i) → E'
  19. Intersect(edgeCG, edgeBG) → I
  20. Line(I, A) → j
  21. Polygon(A, B, E) → poly2, e_1, a_1, b_1
  22. Polygon(J, A, E) → poly4, e_3, j_2, a_2
  23. Mirror(ListPoly, i) → ListPoly'
  24. Sequence(Rotate[ListPoly', (-((n * α))), j], n, 1, 4) → ListPyramid'
  25. Mirror(ListPyramid', i) → ListPyramid''
  26. Polygon(K', E, L) → poly5, k, l, m
  27. Angle(B, E, J) → β
  28. Rotate(F, (-γ), g) → F'
  29. Rotate(A, (-γ), g) → A'
  30. Segment(F', A') → edgeAF'
  31. Rotate(poly5, (-γ), g) → poly5'
  32. Rotate(poly5', (-γ), g) → poly5''
  33. Sequence(Rotate[poly5, ((-n) * γ), g], n, 1, 3) → ListDecoration
  34. Intersect(edgeAF', edgeAH) → M
  35. Line(B, H) → n
  36. Rotate(ListDecoration, (-α), n) → ListDecoration'
  37. Sequence(Rotate[ListDecoration, ((-n) * α), j], n, 1, 4) → ListDecorationRing
  38. Sequence(Rotate[ListDecoration', ((-n) * α), j], n, 1, 4) → ListDecorationRing'